INTERMOLECULAR FORCES AXD INTERACTION ENERGY 229 



Such multipoles cannot be determined experimentally but our knowledge 

 of molecular structure and bond moments make it likely that they occur 

 frequently and play a subsidiary role in intermolecular interactions. They 

 are no longer considered to be the explanation of attraction between neu- 

 tral nondipolar molecules; rather they probably contribute to a minor de- 

 gree in certain cases and are to be thought of in addition to the dispersion 

 forces. Whereas the field strength of a dipole is proportional to Ijd^, that 

 of a quadrupole is proportional to 1/fZ^ and that of an octupole to l/d^. 

 Thus dipole-quadrupole and quadrupole-quadrupole interactions are of 

 significance only when the molecules are quite close. There are also induced 

 multipoles and the B' and B" terms in Eq. 6-49 are due to such effects. 

 Even in interactions between hydrogen atoms the contribution of quad- 

 rupole terms is appreciable in the total dispersion energy. An excellent 

 discussion of quadrupoles and their interactions with ions, dipoles, and 

 other quadrupoles has been given by Buckingham (1959). The quadrupole 

 moments of some simple molecules are given in units of IQ-^e esu: Hg, 

 0.63; N2, ± 1.5; CO, - 3; H^O, 2; NH3, 1; and C2H4, ± 1. 



Short-Range Repulsive Interactions 



Having discussed the various attractive forces between molecules, it 

 is now necessary to treat the repulsive forces that maintain a separation 

 between atoms and molecules. Repulsion can, of course, arise from ion-ion, 

 ion-dipole, and dipole-dipole interactions, and these are undoubtedly of im- 

 portance in certain enzyme reactions. However, the purpose of the present 

 section is to sketch the nature of the general nonspecific repulsive forces 

 that occur whenever atoms or molecules come into contact. When nega- 

 tively charged clouds of electron pairs, such as surround all molecules, begin 

 to interpenetrate, repulsion occurs. It has not yet been possible to treat 

 this problem in a satisfactory manner theoretically but the repulsion con- 

 stants can often be evaluated. It will be satisfactory for our purpose to 

 represent the energy of repulsion as 9? = A/d'^. We may thus write for the 

 total potential energy of a pair of interacting structures: 



V total = Trevulsion + Tattraction = ^jd" - Bid" (6-50) 



when one type of attractive force is dominant; A and B are constants rep- 

 resenting the magnitudes of repulsion and attraction energies and a and 

 b indicate the dependence on the distance of separation. The exponent a 

 is usually high (often between 9 and 15) and is difficult to evaluate accu- 

 rately; it also varies with the electronic nature of the atoms and molecules 

 involved. The product ab and the sum a + b can be approximated by var- 

 ious experimental procedures (Moelwyn-Hughes, 1957, p. 314); usually 

 one knows fairly accurately the value of b, and hence a can be derived. 



